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Archimedes, a scientist from the Ancient Greece, discovered 13 types of polyhedra, called now as Archimedean solids, which are also referred as semi-regular polyhedra.

Each of them is limited by different types of regular polygons where the polyhedral angles and identical polygons are equal. Furthermore, the same number of equal faces meets at each vertex. In the same order each of these solids can be inscribed into a sphere.

Sodium sulphate reminds the shape of tetrahedron.

One can specify the following mathematical characteristics in each of the five Platonic solids:

1. The radius of the sphere circumscribing the polyhedron;

2. The radius of the sphere inscribed in the polyhedron;

3. The surface area of the polyhedron;

4. The volume of the polyhedron.

**polyhedron** is a solid bounded by flat polygons, which are called **faces.** Sides of the faces are called **edges**, and their corners are called as **vertices**. Depending on the number of faces one can specify tetrahedron (4 faces), pentahedron (5 faces), etc. A polyhedron is considered to be **convex** if it is located on one side of the plane of each of its faces. A polyhedron is called **regular** if its faces are regular polygons (i.e., where all sides and angles are equal) and all polyhedral angles at the vertices are equal. There can be found five types of regular polyhedra: tetrahedron, cube (regular hexahedron), octahedron, dodecahedron, icosahedron.

Architects have used the elements of polyhedra in designing their constructions since ancient times. Nowadays this approach distinguishes buildings among thousands of others.

The Ministry of Defense in USA has the shape of a regular pentagon.

Is it possible to make up an icosahedron using more simple polyhedra?

Art. Lebedev Studio has offered a new birdhouse in the form of polyhedron.